We use an argument based on the Tubular Neighborhood Theorem (TBT). Fix any point \(\theta \in \mathcal {M}\)  and let \(B_\theta (\epsilon )\)  be the \(\epsilon \) -ball around \(\theta \)  in the ambient space. By the TBT (see [1]}), any point \(p \in B_\theta (\epsilon )\)  can be written as a linear combination of local coordinates and normal vectors on the manifold. Assume WLOG that \(\epsilon \)  is small enough such that there exists a smooth coordinate chart \((\psi _\theta , \mathcal {U}_\theta )\)  such that \(\mathcal {M} \cap B_\theta (\epsilon ) \subseteq \mathcal {U}_\theta \) . Then,
\( p = \eta (u, v) = \psi ^{-1}_\theta (u) + vQ_{\theta }^\perp , \) 
